| Titre : | Optimal control theory : an introduction / |
| Titre original: | Théorie du contrôle optimal: une introduction |
| Auteurs : | Donald E. Kirk |
| Type de document : | Monographie imprimée |
| Editeur : | Mineola, N.Y. : Dover Publications, 2004 |
| ISBN/ISSN/EAN : | 978-0-486-43484-1 |
| Format : | ix, 452 p. / ill. / 22 cm |
| Note générale : | Originally published: Englewood Cliffs, N.J. : Prentice-Hall, 1970 (Prentice-Hall networks series) |
| Index. décimale : | 003/.5 |
| Catégories : |
[Agneaux] Control theory. [Agneaux] Mathematical optimization. |
| Résumé : | Optimal control theory is the science of maximizing the returns from and minimizing the costs of the operation of physical, social, and economic processes. Geared toward upper-level undergraduates, this text introduces three aspects of optimal control theory: dynamic programming, Pontryagin s minimum principle, and numerical techniques for trajectory optimization. Chapters 1 and 2 focus on describing systems and evaluating their performances. Chapter 3 deals with dynamic programming. The calculus of variations and Pontryagin s minimum principle are the subjects of chapters 4 and 5, and chapter 6 examines iterative numerical techniques for finding optimal controls and trajectories. Numerous problems, intended to introduce additional topics as well as to illustrate basic concepts, |
| Sommaire : |
Describing the System and Evaluating Its Performance
Introduction p. 3 Problem Formulation p. 3 State Variable Representation of Systems p. 16 Concluding Remarks p. 22 References p. 23 Problems p. 23 The Performance Measure p. 29 Performance Measures for Optimal Control Problems p. 29 Selecting a Performance Measure p. 34 Selection of a Performance Measure: The Carrier Landing of a Jet Aircraft p. 42 References p. 47 Problems p. 47 Dynamic Programming Dynamic Programming p. 53 The Optimal Control Law p. 53 The Principle of Optimality p. 54 Application of the Principle of Optimality to Decision-Making p. 55 Dynamic Programming Applied to a Routing Problem p. 56 An Optimal Control System p. 58 Interpolation p. 64 A Recurrence Relation of Dynamic Programming p. 67 Computational Procedure for Solving Control Problems p. 70 Characteristics of Dynamic Programming Solution p. 75 Analytical Results--Discrete Linear Regulator Problems p. 78 The Hamilton-Jacobi-Bellman Equation p. 86 Continuous Linear Regulator Problems p. 90 The Hamilton-Jacobi-Bellman Equation--Some Observations p. 93 Summary p. 94 References p. 95 Problems p. 96 The Calculus of Variations and Pontryagin's Minimum Principle The Calculus of Variations p. 107 Fundamental Concepts p. 108 Functionals of a Single Function p. 123 Functionals Involving Several Independent Functions p. 143 Piecewise-Smooth Extremals p. 154 Constrained Extrema p. 161 Summary p. 177 References p. 178 Problems p. 178 The Variational Approach to Optimal Control Problems p. 184 Necessary Conditions for Optimal Control p. 184 Linear Regulator Problems p. 209 Pontryagin's Minimum Principle and State Inequality Constraints p. 227 Minimum-Time Problems p. 240 Minimum Control-Effort Problems p. 259 Singular Intervals in Optimal Control Problems p. 291 Summary and Conclusions p. 308 References p. 309 Problems p. 310 Iterative Numerical Techniques for Finding Optimal Controls and Trajectories Numerical Determination of Optimal Trajectories p. 329 Two-Point Boundary-Value Problems p. 330 The Method of Steepest Descent p. 331 Variation of Extremals p. 343 Quasilinearization p. 357 Summary of Iterative Techniques for Solving Two-Point Boundary-Value Problems p. 371 Gradient Projection p. 373 References p. 408 Problems p. 409 Conclusion Summation p. 417 The Relationship Between Dynamic Programming and the Minimum Principle p. 417 Summary p. 423 Controller Design p. 425 Conclusion p. 427 References p. 427 Appendices p. 429 Useful Matrix Properties and Definitions p. 429 Difference Equation Representation of Linear Sampled-Data Systems p. 432 Special Types of Euler Equations p. 434 Answers to Selected Problems p. 437 Index p. 443 Table of Contents provided by Ingram. All Rights Reserved. |
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|---|---|---|---|---|---|
| SI8/3109 | Livre | BIB.FAC.ST. | Empruntable | Magazin |
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